1. Field of the Invention
This invention pertains generally to management of glucose and insulin delivery levels to mimic a natural beta cell, and more particularly, to an apparatus and method using a run-to-run algorithm for episodic basal and bolus insulin dosing and monitoring of plasma glucose levels.
2. Incorporation by Reference of Publications
The following publications referenced herein using numbers inside brackets (e.g., [1]) are incorporated by reference herein in their entirety:
[1] T. Mandrup-Poulsen, “Recent advances: Diabetes,” Br. Med. J., vol. 316, pp. 1221-1225, April 1998.
[2] American Diabetes Association, “Standards of medical care for patients with diabetes mellitus,” Diabetes Care, vol. 26, pp. S33-S50, 2003.
[3] Diabetes Control and Complications Trial Research Group, “The effect of intensive treatment of diabetes on the development and progression of long-term complications in insulin-dependent diabetes mellitus,” N. Engl. J. Med., vol. 329, pp. 977-986, September 1993.
[4] American Diabetes Association, “Standards of medical care for patients with diabetes mellitus,” Diabetes Care, vol. 26, pp. S33-S50, January 2003.
[5] L. Jovanovic and C. Peterson, “Home blood glucose monitoring,” Comp. Ther., vol. 8, pp. 10-20, January 1982.
[6] L. Chanoch, L. Jovanovic, and C. Peterson, “The evaluation of a pocket computer as an aid to insulin dose determination by patients,” Diabetes Care, vol. 8, pp. 172-176, March/April 1982.
[7] A. Schiffrin, M. Mihic, B. Leibel, and A. Albisser, “Computer-assisted insulin dosage adjustment,” Diabetes Care, vol. 8, pp. 545-552, November/December 1985.
[8] F. Chiarelli, S. Tumini, G. Morgese, and A. Albisser, “Controlled study in diabetic children comparing insulin-dosage adjustment by manual and computer algorithms,” Diabetes Care, vol. 13, pp. 1080-1084, 1990.
[9] C. Mao, M. Riegelhuth, D. Gundy, C. Cortez, S. Melendez, and E. Ipp, “An overnight insulin infusion algorithm provides morning normoglycemia and can be used to predict insulin requirements in noninsulin-dependent diabetes mellitus,” J. Clin. Endo. Metab., vol. 82, pp. 2466-2470, April 1997.
[10] A. Albisser, “Toward algorithms in diabetes self-management,” Diab. Tech. Ther., vol. 5, pp. 371-373, 2003.
[11] J. Moyne, E. del Castillo, and A. Hurwitz, Run-to-run Control in Semiconductor Manufacturing. New York, N.Y.: CRC Press, 2001.
[12] K. Lee, I. Chin, and H. Lee, “Model predictive control technique combined with iterative learning for batch processes,” AlChE J., vol. 45, pp. 2175-2187, 1999.
[13] R. Bergman, L. Phillips, and C. Cobelli, “Physiologic evaluation of factors controlling glucose tolerance in man,” J. Clin. Invest., vol. 68, pp. 1456-1467, 1981.
[14] R. Bergman, Y. Ider, C. Bowden, and C. Cobelli, “Quantitative estimation of insulin sensitivity,” Am. J. Physiol., vol. 236, pp. E667-E677, 1979.
[15] J. Sorensen, “A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes,” Ph.D. dissertation, Massachusetts Institute of Technology, Boston, 1985.
[16] R. Parker and F. Doyle III, “Control-relevant modeling in drug delivery,” Adv. Drug Deliv. Rev., vol. 48, pp. 211-228, 2001.
[17] M. Berger and D. Rodbard, “Computer simulation of plasma insulin and glucose dynamics after subcutaneous insulin injection,” Diabetes Care, vol. 12, pp. 725-736, November/December 1989.
[18] S. Arimoto, S. Kawamura, and F. Miyazaki, “Bettering operation of dynamic systems by learning: A new control theory for servomechanism or mechatronics systems,” in Proc. IEEE 23rd Conference on Decision and Control, Las Vegas, Nev., Dec. 1984, pp. 1064-1069.
[19] N. Amann, D. Owens, and E. Rogers, “Iterative learning control for discrete-time systems with exponential rate of convergence,” in Proc. IEE Control Theory Appl., Dearborn, Mich., March 1996, pp. 217-224.
[20] K. Lee, S. Bang, and K. Chang, “Feedback-assisted iterative learning control based on an inverse process model,” J. Proc. Cont., vol. 4, pp. 77-89, May 1994.
[21] J. Lee, K. Lee, and W. Kim, “Model-based iterative learning control with a quadratic criterion for time-varying linear systems,” Automatica, vol. 36, pp. 641-657, May 2000.
[22] B. Srinivasan, C. Primus, D. Bonvin, and N. Ricker, “Run-to-run optimization via control of generalized constraints,” Contr. Eng. Prac., vol. 9, pp. 911-919, 2001.
[23] B. Srinivasan, S. Palanki, and D. Bonvin, “Dynamic optimization of batch process. I. Characterization of the nominal solution,” Comp. Chem. Eng., vol. 27, pp. 1-26, 2002.
[24] B. Srinivasan, D. Bonvin, E. Visser, and S. Palanki, “Dynamic optimization of batch processes. II. Role of measurements in handling uncertainty,” Comp. Chem. Eng., vol. 27, pp. 27-44, 2002.
[25] Cook C B, Mann L J, King E C, New K M, Vaughn P S, Dames F D, Dunbar V G, Caudle J M, Tsui C, George C D, McMichael J P: Management of insulin therapy in urban diabetes patients is facilitated by use of an intelligent dosing system. Diabetes Technol Ther 2004; 6:326-335.
[26] Gopakumaran B: Intelligent dosing system: a useful computer program for diabetic management? Diabetes Technol Ther 2004; 6:336-338.
[27] Gross T, Kayne D, King A, Rother C, Juth S: A bolus calculator is an effective means of controlling postprandial glycemia in patients on insulin pump therapy. Diabetes Technol. Ther. 2003; 5:365-369.
3. Description of Related Art
Diabetes mellitus affects over 100 million individuals worldwide, and this number is expected to double by 2010 [1]. In the US, the estimated healthcare costs of the 12 million affected is estimate to be 136 billion dollars annually. Diabetes mellitus is a disorder of the metabolism that is characterized by the inability of the pancreas to secrete sufficient amounts of insulin [2]. Insufficient amounts of insulin results in large fluctuations in blood glucose levels can have both short-term and long-term physiological consequences. Long-term complications arising from elevated blood glucose levels (hyperglycemia) in patients with Type 1 diabetes include retinopathy, neuropathy, nephropathy and other vascular complications. Low glucose levels (hypoglycemia) can lead to diabetic coma, seizures, accidents, anoxia, brain damage, decreased cognitive function, and death.
The conventional approach to glucose regulation in diabetic patients includes 3-5 daily insulin injections, with the quantity of insulin being determined by 4-8 invasive blood glucose measurements each day. This method of insulin delivery is painful, inconvenient and may be unreliable due to the pharmacokinetics of the insulin analogues that are typically used. Pen devices have been developed to make insulin delivery more convenient; however, the inability to mix insulin or insulin analogue types is a disadvantage. Several other routes of insulin delivery have been studied as an alternative to insulin injections including inhalation and transdermal insulin delivery. Others have explored the efficacy of continuous subcutaneous insulin infusion (CSII) using a pump. This has mainly been done in comparison to conventional insulin therapy or multiple daily insulin injections (MDI). Continuous subcutaneous insulin infusions by external insulin infusion pumps normally use rapid-acting insulin analogues.
Typical fixed dosage approaches assume that the metabolic demands of each day are metabolically similar, and that the fixed dosages adequately anticipate the timing and quantity of insulin that is required by the patient.
Unfortunately, blood glucose fluctuations continue to occur uncontrollably in many patients beyond the normal range of 60-120 mg/dl, exacerbating the risks of physical complications. Periodic episodes of hypoglycemia and hyperglycemia may occur when the insulin needs of the patient deviate from the levels predicted by regimen and present in the bloodstream.
The development of external insulin infusion pumps, along with the introduction of rapid acting insulin analogs has greatly aided in making intensive insulin therapy feasible. The efficacy of the insulin therapy is quantified by measurement of the percentage of glycosylated hemoglobin in the bloodstream (A1C). Values less than 6% are seen in normal healthy people without diabetes; whereas, higher percentages are indicative of sustained hyperglycemia [4].
Several algorithms have been developed to optimize the insulin therapy of people with diabetes. Jovanovic et al. proposed several insulin delivery logic rules for an NPH/Regular insulin system, a Lente insulin system and a constant subcutaneous insulin infusion system [5]. Heuristics were determined to account for food intake, weight loss, exercise, childhood, adolescence and pregnancy. Chanoch et al. evaluated the use of a pocket computer to aid in determining the proper insulin dose for people with diabetes [6]. Patient specific parameters such as weight, gender and physical activity along with carbohydrate content of meals and blood glucose measurements were used by the algorithm to optimize the insulin dose.
With use of the pocket computer, A1C values decreased from 7.2% to 5.8%, with a resulting mean blood glucose of 130 mg/dl versus 160 mg/dl before the study. Schiffren et al. also explored the use of computer algorithms for insulin dose adjustment [7]. Seven patients with type 1 diabetes were recruited to use the computer algorithm for an eight week period. During the control period, the mean blood glucose concentration for all patients was 178, 187, 208, and 207 mg/dl for breakfast, lunch, dinner and bedtime snack pre-meal measurements. Upon completion of the algorithm phase of the study, these values decreased to 116, 110, 148, and 135 mg/dl, respectively, for the same pre-meal measurements. Chiarelli et al. investigated the use of a computer algorithm in children [8]. Their results showed fewer episodes of hypoglycemia in the computer-assisted group. Other studies have employed the use of computer algorithms to maintain normal glycemia levels in patients with hyperglycemia, insulin-resistance and type 2 diabetes [9]. Albisser highlighted several algorithms that have been developed to aid in the progress of self-management of diabetes for better blood glucose control [10].
A number of virtual patient models for diabetes exist in the literature. The work that is described in the following sections emphasizes results evaluated on the Bergman model. In addition, the Sorensen and Automated Insulin Dosage Advisor (AIDA) models have been investigated, and those results are highlighted to emphasize the applicability of the run-to-run algorithm to different virtual patient systems.
The Bergman model is a three compartment minimal model of glucose and insulin dynamics [13]. This 3rd-order model is comprised of a glucose compartment, G, a remote insulin compartment, X, and an insulin compartment, I [14]. The remote insulin compartment mediates glucose uptake within the glucose space to the peripheral and hepatic tissues. The insulin distribution space combines the sinks and sources of insulin production and consumption into a single pool. While the Bergman model is simplistic in nature, it is able to capture certain dynamics of the diabetic patient system. The insulin dynamics of the Bergman model are driven by an intravenous infusion of insulin to the system.
The Sorensen model is a 6-compartment model [15], [16]. The compartments are physiological representations of the brain, heart and lungs, liver, gut, kidney and peripheral tissue. Within the brain and peripheral tissue, both the dynamics within the interstitial fluid and capillary fluid are detailed. The glucose meal disturbance is ingested directly into the gut accompanied by intravenous delivery of insulin and arterial blood glucose measurements. This 21st order model describes glucose, insulin and glucagon dynamics of the diabetic patient. Similar to the Bergman model, the Sorensen model relies on an intravenous infusion of insulin to drive the insulin dynamics of the system. Due to the incorporation of glucagon's action to promote hepatic output of glucose into the model, blood glucose levels do not remain in the hypoglycemic range for extended periods of time.
The Automated Insulin Dosage Advisor (AIDA) is a 4th-order 3-compartment model of insulin and glucose dynamics. In contrast to the Bergman model, the insulin dynamics of the model are driven by subcutaneous injection of insulin [17]. The AIDA model was first proposed as an educational tool. Hence, the model does attempt to model the effects of different meal sizes on the rate of gastric emptying in the system. The AIDA model was also originally designed to reflect the use of several different insulin analogs on the insulin therapy of an individual. In doing so, subcutaneous transport dynamics were accounted for to simulate the effect of a subcutaneous injection of insulin to the body. The AIDA model was developed in the spirit of the minimal model approach, resulting in few patient specific parameters.
Run-to-run control (or batch) control has been commonly used in industrial batch processes, such as semiconductor manufacturing [11]. In run-to-run control, information about product quality from the previous run is used to determine the input for the next run [12].
Arimoto et al. proposed the “betterment process” concept as a measure of making the inputs for certain systems, such as mechanical robots, yield better outputs [18]. The concept can be applied to multi-input multi-output systems that have a repetitive or cyclic behavior. The convergence properties of this iterative learning control algorithm were studied by Amann et al. [19]. Using an inverse process model, Lee et al. derived a feedback-assisted iterative learning control scheme (FBALC) to attain the maximum convergence rate [20]. This approach was evaluated on a simulated bench-scale batch reactor, to demonstrate the ability of the algorithm to control reactor temperature. For time-varying linear constrained systems, prevalent in the chemical process control area, Lee et al. proposed a model-based iterative learning control scheme with a quadratic performance objective [21]. The feasibility of this algorithm in the presence of disturbances and noise was tested on several numerical examples. Lee et al. have also combined model predictive control with iterative learning control [12]. In doing so, the algorithm can accommodate both within-run and run-to-run errors. Srinivasan et al. proposed a constraint control scheme in the run-to-run framework to optimize the operation of a batch process and this approach is investigated in the present study for glucose control [22], [23], [24].
Insulin-dosing algorithms have been used in several commercially available products. For example, the Intelligent Dosing System (IDS™, Dimensional Dosing Systems, Wexford, Pa.) proposed by Cook et al. [25] has been used by clinicians to update the insulin therapy of patients on a month-to-month basis. The algorithm uses a nonlinear control law that relies on the glucose measurements (fasting or random glucose) and/or A1C values to determine the correct total daily dose of insulin. The insulin dose is determined such that the desired glucose measurement or A1C value is achieved at the next visit. This algorithm only makes recommendations to increase the total daily insulin dose; hence, the algorithm is one sided and does not address all aspects of the insulin therapy of the patient [26].
Another bolus dosing algorithm is the Bolus Wizard™ calculator (Medtronic Minimed, Northridge, Calif.), which allows the patient to set various blood glucose targets throughout the day [27]. The algorithm relies on blood glucose measurements, carbohydrate ratios, and insulin sensitivity factors to update the insulin therapy of a patient. The algorithm also accounts for the amount of active insulin in the body with the use of an insulin action curve.
However, existing insulin therapy schemes do not account for variations in meal composition, routines, physical activity and other influences on the insulin requirements of a patient. As a result, the insulin needs of the patient may still deviate from the levels predicted by regimen and present in the bloodstream, resulting in periodic episodes of hypoglycemia and hyperglycemia.
Accordingly, there is a need for a therapy for a patient with type 1 diabetes that permits the administration of insulin that mimics the physiologic needs of the patient and the normal insulin levels of a non-diabetic.